Vladislav Lesnikov

Vyatka State University · Applied Mathematics and Telecommunications

Earlier it was found that the zeros and poles of IIR digital filters with finite word length are elements of the set of algebraic numbers. Therefore, not every point of the unit circle of the z-plane can be a zero and / or a pole of such digital filters. The position of admissible positions for zeros and poles depends on the degree of algebraic num...

Abstract— At the end of the 20th century, even with the use of various flight safety systems such as IFF, ATCRBS and ACAS, there were a significant number of airplanes and other aircraft crushes in the air, which necessitated the improvement of these systems. These improvements were reflected in the MODE-S technology. Nowadays every civilian aircra...

Despite the simplicity of the energy detector, its use in cognitive radio systems is limited by the need of a priori information about the noise level. In the absence of such information, it is necessary to estimate the variance of the noise in one way or another and recalculate the threshold of detection on false alarm. If the noise is additive wh...

One of parts of digital signal processing is processing with undersampling. In this case, the sampling frequency is lower, than it is required by the sampling theorem. At undersampling, the spectrum of signals is distorted by an aliasing. Various ways of correction of the arising distortions are known. These ways are known under the name the unalia...

It is shown that the location of zeros and poles of digital filters with reduced word length could not be arbitrary. The zeros and poles of such filters are the elements of the set of algebraic numbers. The configuration of possible provisions of algebraic numbers of the second degree is considered. Systems of coordinates for the description of top...

In this paper, number-theoretic and algebraic aspects of a choice of the block diagram of the IIR digital filter are considered. It is supposed that generation of structures of digital filters is carried out. The structure of the filter is described by a topological matrix of transfer coefficients between block diagram nodes. It is considered that...

Distributed arithmetic has been widely used for area-time efficient implementation of inner products. It is a bit-serial computational operation that forms an inner product of a pair of vectors in a single direct step. If the word length of the vectors is large, the sequential implementation of the distributed arithmetic require a large number of s...

Distributed arithmetic is a technique developed for the real-time computation of the inner product of the vector with constant elements and the vector with varying coefficients. The inner product is computed without splitting into operations of multiplication and addition. At calculation, operations of summation and shift of inner products of an un...

Criterion for the BIBO stability of the IIR digital filters is well known. IIR filter is BIBO stable if and only if all of its poles are strictly inside the unit circle in the complex z-plane. To analyze the stability of biquad filters in the space of coefficients is constructed the famous triangle of stability. In this paper, this criterion extend...

For the adequate description of digital filters with arbitrary structure it is convenient to use so-called topological matrixes. Elements of these matrixes are transmission coefficients between corresponding nodes of the block diagram. Methods of the analysis of power of round-off noise in the digital filters, based on state-space representation of...

The paper is devoted to technique of comparison of various structures of IIR digital filters on complexity taking into consideration the accuracy of implementation of characteristics. An offered technique is based on dividing of all possible structures into classes of equivalence. All structures belonging to the same equivalence class have the same...

Implementation of canonical structures of IIR digital filters demands execution of the minimum number of operations. Thus these filters can realize any transfer function. Therefore they represent considerable interest at implementation by using FPGA and ASIC. Researches have shown that except widely known classical canonical forms there are also ot...

A new method of the recursive digital filters design is presented. It is based on the application of the number-theoretical and algebraic aspects in the design at functional and structural levels. This paradigm is focused on implementation of digital filters in FPGA and ASIC.

The technique of synthesis of structures of second-order IIR digital filters with general transfer function with the minimal number of nodes, multipliers and delay elements is offered.